\relax 
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand*\HyPL@Entry[1]{}
\HyPL@Entry{0<</S/D>>}
\@writefile{toc}{\contentsline {section}{\tocsection {}{1}{Complex abelian integral on elliptic curves}}{2}{section.1}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.1}{Building blocks of functions on ${\mathbb  {C}}$ associate to a lattice}}{2}{subsection.1.1}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.2}{Abel theory}}{3}{subsection.1.2}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.3}{Rational differential forms on $E$}}{3}{subsection.1.3}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.4}{Algebraic universal extension}}{5}{subsection.1.4}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{1.5}{Weil pairing}}{7}{subsection.1.5}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{2}{Complex abelian integral on algebraic curves}}{8}{section.2}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.1}{Algebraic curve over ${\mathbb  {C}}$}}{8}{subsection.2.1}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces $4g$-gon}}{8}{figure.1}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{2.2}{Differential forms}}{10}{subsection.2.2}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{3}{$p$-adic fields}}{11}{section.3}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.1}{$p$-adic number}}{11}{subsection.3.1}}
\newlabel{thm:hensel}{{3.5}{12}{Hensel's lemma\relax }{thm.3.5}{}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.2}{No $2\pi i$ in ${\mathbb  {C}}_p$}}{14}{subsection.3.2}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.3}{$p$-adic logarithm}}{14}{subsection.3.3}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{3.4}{Cyclotomic extension}}{15}{subsection.3.4}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{4}{Fontaine's rings and $p$-adic Galois representations}}{16}{section.4}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{4.1}{$p$-rings}}{16}{subsection.4.1}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{4.2}{Teichm\"uller representatives}}{16}{subsection.4.2}}
\newlabel{lem:WI}{{4.13}{17}{\relax }{thm.4.13}{}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{4.3}{The ring $\setbox \z@ \hbox {\frozen@everymath \@emptytoks \mathsurround \z@ $\textstyle E$}\mathaccent "055D{E}^+$}}{18}{subsection.4.3}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{4.4}{The ring $\setbox \z@ \hbox {\frozen@everymath \@emptytoks \mathsurround \z@ $\textstyle A$}\mathaccent "055D{A}^+=W(\setbox \z@ \hbox {\frozen@everymath \@emptytoks \mathsurround \z@ $\textstyle E$}\mathaccent "055D{E}^+)$}}{19}{subsection.4.4}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{4.5}{The ring $B_{{\mathrm  {dR}}}^+$ and the field $B_{\mathrm  {dR}}$}}{19}{subsection.4.5}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{4.6}{$p$-adic Galois representation}}{21}{subsection.4.6}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{5}{$p$-adic abelian integral}}{22}{section.5}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.1}{Lubin-Tate formal groups}}{22}{subsection.5.1}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.2}{Periods of Lubin-Tate groups}}{25}{subsection.5.2}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.3}{$p$-adic integration}}{27}{subsection.5.3}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.4}{$p$-adic periods of abelian integrals}}{29}{subsection.5.4}}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.5}{$p$-adic Riemann relations}}{30}{subsection.5.5}}
\newlabel{tocindent-1}{0pt}
\newlabel{tocindent0}{0pt}
\newlabel{tocindent1}{17.77782pt}
\newlabel{tocindent2}{29.38873pt}
\newlabel{tocindent3}{0pt}
\@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.6}{One example of application}}{31}{subsection.5.6}}
